Last month (August 2009, p. 104) we posted a trio of brainteasers, including one as yet unsolved, concerning probability and intuition.
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On the first puzzle, I can't seem to come up the probability of 0.5254.
Probability of one specific instance not happening - call this x
x = (1 - 1 / (38 ** 3)) =
Number of possible instances - call this y
y = 105 * 104 * 103 / (3 * 2)
Probability of none of the instances happening - call this z
z = x ** y
Probability of at least one instance happening (i.e probability of coming out ahead) - (1 - z)
Google for -
1 - ((1 - (1 / (38 ** 3))) ** (105 * 104 * 103 / (3 * 2)))
You get 0.967167798
What did I do wrong? Or is this a calculator precision problem?
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